Great rhombated demitesseract

Great rhombated demitesseract
Rank	4
Type	Semi-uniform
Notation
Coxeter diagram	x3y3o *b3z
Elements
Cells	8+8 truncated tetrahedra, 8 great rhombitetratetrahedra
Faces	32 triangles, 24 rectangles, 32+32 ditrigons
Edges	48+48+96
Vertices	96
Vertex figure	Sphenoid
Measures (edge lengths a (of triangles), b, c (of rectangles))
Circumradius	${\sqrt {\frac {2a^{2}+b^{2}+c^{2}+2ab+2ac+bc}{2}}}$
Dichoral angles	Tut–3–tut: 120°
	Gratet–6–tut: 120°
	Gratet–4–gratet: 90°
Central density	1
Related polytopes
Dual	Sphenoidal enneacontihexachoron
Conjugate	Great rhombated demitesseract
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	D4, order 192
Convex	Yes
Nature	Tame

The great rhombated demitesseract or runcicantic tesseract is a convex semi-uniform polychoron that is a variant of the tesseractihexadecachoron with demitesseractic symmetry. As such it can be represented by x3y3o *b3z, and has 16 truncated tetrahedra (of two types, forms x3y3o and z3y3o) and 8 great rhombitetrahedra (type x3y3z) as cells, with 3 edge lengths.

Vertex coordinates

A great rhombated demitesseract with edge lengths a, b, and c has vertices given by all permutations and even sign changes of:

• $\left((a+2b+2c){\frac {\sqrt {2}}{4}},\,(a+2b){\frac {\sqrt {2}}{4}},\,a{\frac {\sqrt {2}}{4}},\,a{\frac {\sqrt {2}}{4}}\right).$

Alternative coordinates in a different orientation can be given by all even sign changes and permutations of:

• $\left((a+2b+c){\frac {\sqrt {2}}{4}},\,(a+2b+c){\frac {\sqrt {2}}{4}},\,(a+c){\frac {\sqrt {2}}{4}},\,(a-c){\frac {\sqrt {2}}{4}}\right).$